If the line lx+my=1 is a tangent line to the circle x^{2}+y^{2}=a2, the locus of (l,m) is
The coefficients of three successive terms in the expansion of (1 + x)^{n} are 165, 330 and 462 respectively, then the value of n will be
Let coefficients of three consecutive terms i.e., (r + 1)th, (r + 2)th and (r + 3)th in expansion of (1 + x)^{n} are 165.330 and 462 respectively then
coefficient of (r + 1)th term = ^{n}C_{r} = 165
coefficient of (r + 2)th term = ^{n}C_{r + 1} = 330
coefficient of (r + 3)th term = ^{n}C_{r + 2} = 462
∴ n C r + 1 n C r = n  r r + 1 = 2
or, n  r = 2(r + 1)
or, r = 1 3 (n  2)
and n C r + 2 n C r + 1 = n  r  1 r + 2 = 231 165
or, 165(n  r  1) = 231 (r + 2)
or, 165n  627 = 396r
or, 165n  627 = 396 x 1 3 (n  2)
or, 165n  627 = 132 (n  2)
or, 33n = 363
∴ n = 11
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I
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Statement2 :
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